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EXTENSION OF COHOMOLOGY CLASSES FOR VECTOR BUNDLES WITH SINGULAR HERMITIAN METRICS

Part of: (Co)homology theory Holomorphic fiber spaces Holomorphic convexity Analytic spaces

Published online by Cambridge University Press:  17 February 2025

ZHUO LIU Open the ORCID record for ZHUO LIU [Opens in a new window]  and
CHENGHAO QING Open the ORCID record for CHENGHAO QING [Opens in a new window]
ZHUO LIU
Affiliation:
Mathematical Science Research Center Chongqing University of Technology No. 69, Hongguang Avenue, Banan District Chongqing China email:[email protected]
CHENGHAO QING*
Affiliation:
Yau Mathematical Sciences Center Tsinghua University 30 Shuangqing Road, Haidian District Beijing China
*
[email protected]
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Abstract

In this paper, we present an extension theorem which is equivalent to an injectivity theorem on the cohomology groups of vector bundles equipped with singular Hermitian metrics over holomorphically convex Kähler manifolds.

Keywords

extension theoremcohomology groupvector bundlemultiplier submodule sheafsingular Hermitian metric

MSC classification

Primary: 32C35: Analytic sheaves and cohomology groups
Secondary: 14F18: Multiplier ideals 32E05: Holomorphically convex complex spaces, reduction theory 32L10: Sheaves and cohomology of sections of holomorphic vector bundles, general results 32L20: Vanishing theorems
Type
Article
Information
Nagoya Mathematical Journal , First View , pp. 1 - 19
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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